Three points A, B and C lie in this order on a line, and P is any point in the plane. Use the Cosine Rule to prove the following statement.
Take any pair of two digit numbers x=ab and y=cd where, without loss of generality, ab > cd . Form two 4 digit numbers r=abcd and s=cdab and calculate: {r^2 - s^2} /{x^2 - y^2}.
Find the polynomial p(x) with integer coefficients such that one solution of the equation p(x)=0 is $1+\sqrt 2+\sqrt 3$.
Your answer will depend on the length and breadth of the table, but does it depend on where the ball is to start with?
Don't be too quick to accept this diagram - what assumptions might it be useful to make about the rebound angles?
Now use that to draw your own diagram.